Question

Help me please in Algebra! :/ will give a medal!

Tori works two jobs to pay for college. She tutors for $30 per hour and also works as a receptionist for $10 per hour. Due to her class and study schedule, Tori is only able to work up to 20 hours per week, but must earn at least $200 per week. If t represents the number of hours Tori tutors and r represents the number of hours she works as a receptionist, which system of inequalities represents this scenario?

a. t + r greater than or equal to 20
30t + 10r = 200

b. t + r less than or greater to 20
30t + 10r less than or greater to 200

c. t + r less than or greater to 20
30t + 10r = 200

d. t + r less than or greater to 20
30t + 10r greater than or equal to 200

Answer 1

Now, from here, you have to put the values that relate to each other together; the amount of time she works from job t + r (<or=to) 20. We get the sign from the statement "she is ONLY able to work UP TO 20hrs).

Answer 2

I messed up the parenthesis at the end
<mfw doh

Answer 3

Wait, i am confused now, would the answer be b?

Answer 4

Why do you eliminate the answer c? It has the top portion answer.

Answer 5

Ohhhh okay i see! i had to reread that answer :) Thank you so much can you help me with another question??

Answer 6

Of course. :)

Answer 7

Thank you so much! these are the ones i do not understand at all. :/


1.Sally has only nickels and dimes in her money box. She knows that she has less than $20 in the box. Let x represent the number of nickels in the box and y represent the number of dimes in the box. Which of the following statements best describes the steps to graph the solution to the inequality in x and y?

Draw a dashed line to represent the graph of 5x + 10y = 2000 and shade the portion above the line for positive values of x and y.

Draw a dashed line to represent the graph of 10x + 5y = 2000 and shade the portion above the line for positive values of x and y.

Draw a dashed line to represent the graph of 5x + 10y = 2000 and shade the portion below the line for positive values of x and y.

Draw a dashed line to represent the graph of 10x – 5y = 2000 and shade the portion below the line for positive values of x and y.

2.Which of the following statements best describes the graph of –5x + 2y = 1?

a. It is a curve joining the points (–5, 2), (2, 3), and (4, 1).

b. It is a curve joining the points (–1, –3), (–1, –3), and (1, 5).

c. It is a straight line joining the points (1, 3), (3, 8), and (–3, –7).

d. It is a straight line joining the points (4, –3), (–1, 2), and (–4, 5).

3.)Sam and Harry are family. Sam is currently is three times Harry's age. Sam's age is also 10 more than twice Henry's age. What are their current ages?

a. Sam is 24 years old, and Harry is 8 years old.

b. Sam is 39 years old, and Harry is 13 years old.

c. Sam is 27 years old, and Harry is 9 years old.

d. Sam is 30 years old, and Harry is 10 years old.

4.)A system of equations is shown below:

6x – 2y = 3 (equation 1)
5x + 3y = 4 (equation 2)

A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?

a. Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

b.Show that the solution to the system of equations 10x – 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

c. Show that the solution to the system of equations 11x – y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

d.Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Answer 8

For the following system, if you isolated x in the second equation to use the Substitution Method, what expression would you substitute into the first equation?

3x + y = 8
-x - 2y = -10

a. -2y + 10

b. 2y + 10

c. 2y - 10

d. -2y - 10

6.)Solve the following system of equations:
x - 2y = 5
2x - 4y = 10

a. Infinitely many solutions

b. No solutions

c. (0, 0)

d. (5, 10)


These are the last 2.

Answer 9

Hi i am so sorry, internet went out :/

Answer 10

Sorry, server d/c. Now, we know that "she know she has LESS than $20". What does this mean the sign could be/is?

Answer 11

subtraction? :o

Answer 12

Ok, so lets take it from the top. The box itself contains dimes and nickels. We don't know how many, but we do know that the value of a dime is $.10 and nickel is $.05, yes?

Answer 13

yes!

Answer 14

Now, from then, the girl believes that, regardless of the combination, it will amount to a value LESS than $20 (its given).

Answer 15

With me?

Answer 16

Yes i am

Answer 17

They want us to represent nickels as x, and dimes with y (stated in problem). So, we may make an equation: \[.05x+.10y<20\]

Answer 18

Okay i most definitely understand the equation part :)

Answer 19

Now, for no reason, they got rid of the decimals by multiplying everything by 100
\[(.05x+.10y<20)*100\rightarrow 5x+10t<2000\]

Answer 20

Ohhhh so that is how the 2000 cam in because they multiplied by 100!

Answer 21

Indeed, and you can do ANYTHING to a function so long as you do it to BOTH sides of the equal sign. The second question I can't help with (I forgot how to do it), however, the third is a little complex.

Answer 22

Alright thats ok but wait is the answer b for the question we just worked on?

Answer 23

Sam is 3times the age of Harry. We also know that Sam is 10 + 2times the age of Harry. What 2 equations can we make from this? And no, she said that "she knows that there are LESS than $20 in the box"; if it was shaded above the line, the statement would read "she knows the has MORE than.." (but it doesn't).

Answer 24

so it is c? correct?

Answer 25

Indeed, also, what 2 equations can be made from 3?

Answer 26

it can be 3x+2=10? is that one of them?

Answer 27

Tip, whenever you see the word "is", substitute it with an equal sign. We can do this because when you read off 2=2, you say "2 IS equal to 2". There are 2 different statements.

Answer 28

confusedd :/

Answer 29

Sam's age = 3*age of harry. Sam = 10+2* age of harry. We can us s for Sam's age and h for Harry's age:\[s=3h \left| \right| s= 10+2h\]

Answer 30

ohhhhhh ok ok

Answer 31

What method do you wish to get rid of one of the 2 variables (h or s)?

Answer 32

There is substitution and elimination; substitution is easier, honestly.

Answer 33

S

Answer 34

& yes u believe distribution is the easiest

Answer 35

I*

Answer 36

Good:), now since s=3h, and s also =10+2h, we can SUBSTITUTE in s=3h for the s in the equation s=10+2h:
\[s=3h \left| \right| s=10+2h \rightarrow 3h=10+2h\]
Now we get h alone:\[3h=2h+10\rightarrow h=10\]
Now that we have Harry's age, what can we do to find Sam's?

Answer 37

Do we also substitue for Sam's now?

Answer 38

You got it:)

Answer 39

wouldnt it be 3h=10+2h?

Answer 40

That's what we did to find Harry's age; we got the answer to be h=10. Now that we know that h=10, we put that in into any of the original equations.\[s=3h \left| \right| h=10\rightarrow s=3(10)\rightarrow s=30\]

Answer 41

ahh so all we had to do really was multiply 3 by 10 to get 30, so it is d!

Answer 42

Indeed, I really don't know what's happening in #4, but for the one after that, all it is asking is when you get x alone, what does it equal?

Answer 43

d?

Answer 44

Post how you did it, and I'll post how I did it. :)

Answer 45

well it's pretty simple. if i DID get it right.. if you isolate the (x), all you have is -2y=10 correct?

Answer 46

for the second equation

Answer 47

When you isolate x, you're not getting rid of it, you're making it alone: \[-x-2y=-10\rightarrow -x=2y-10\rightarrow x=-2y+10\]

Answer 48

Upon isolating an equation, you MUST follow reverse PEMDAS, so you would subtract or add first, then divide/multiply ect.

Answer 49

ohhh, i see why it had to be come a plus instead of a subtraction now in the problem you just showed me

Answer 50

Just something for thought, when you have 2 equations that are EXACTLY the same, how many points do they have in common? Say you would have to graph y=x and y=x.

Answer 51

ok m thinking 2 or 4 points?

Answer 52

If 2 functions are the same, they would overlap, would they not?

Answer 53

Oh, ok i understand :)

Answer 54

Now, when you get y alone for both equations, you see that they are the same, which tells us what about the intersections?

Answer 55

They will always overlap?

Answer 56

or intersect? hehe

Answer 57

Indeed, which means what about their points? How many times do they overlap?

Answer 58

well you did say that all points in common will intersect right?

Answer 59

I worded that wrong, but yes! They always intersect, infinite solutions.

Answer 60

Alright thankyou so much!!!! you were a huge helppp :)

Answer 61

Glad to be of use :), feel free to pst me if you need more assistance, have a nice day. :)